Turkiye Cumhuriyeti is a Romanization of the Turkish name for the Republic of Turkey; a Turkiye Cumhuriyeti coin is simply a coin issued by the Turkish government. The currency of Turkey is the lira, which can be divided into kurus.
The lira in use in Turkey today is not the same monetary unit that the Republic of Turkey originally adopted upon its formation in 1922. To combat high inflation, the lira was briefly switched out for the new lira (worth 1,000,000 lira) in 2003. However, the "new" was dropped in 2009 even though the different value was not.
The Republic of Turkey presently manufactures 1, 5, 10, 25 and 50 kurus coins. One lira (100 kurus) coins also exist.